Magneto-optic Phenomenon. 297 



The intensity of the light emerging from the analyser after 

 the minimum rotation $f a is, referring back to the first 

 formula of all, § 3, 



(h(/>. p sin 3> + fi. sin m.) 2 . 



If we turn the analyser out of the minimum position through 

 an angle e, the intensity alters by/V 2 . As a slight alteration 

 of intensity can be the more easily observed the smaller the 

 original intensity, it follows that the accuracy with which the 

 minimum rotations can be observed is greatest at small and 

 large angles of incidence, and is smallest in the neighbourhood 

 of the polarizing angle, where the total intensity is greatest. 

 This accuracy is not the same for positive and negative mag- 

 netization, excepting when (f>. , <j> w <j>. , <f) la are equal to 

 zero. 



5. The positions of the Nicol prisms in which the light 

 reflected from the magnetized mirror is extinguished by the 

 analyser, that is the " zero rotations," are deduced from the 

 formulae for the intensity obtained in § 3. 



These give : — 



f4>% 1 /*<*>? sin 30 



cot m { = - 'TS -±- + cot d>, //, . = - - ?? 



^sid$ ri sinm. I 



cot m t = —P-j 9 - r-^ + cot <£> fi,= - l f— 



If the amplitude p,, and not the phase m, of the magnetic 

 component of the light alters its sign with the direction of 

 magnetization, we can replace (/>? a &c. in equations (4) above 

 by the angles ^° ia . . . . , between the zero-positions of the 

 Nicol prisms for positive and negative magnetization, these 

 latter angles being twice as great as the former. We thus 

 obtain a factor 2 in the numerator of the equations for /^ and 

 fju r Now it can easily be proved that the zero-rotations can 

 be most accurately observed when sin <I> (<£ = difference of 

 phase on reflexion from the metal) is greatest ; that is, in the 

 vicinity of the polarizing angle. At the polarizing angle the 

 zero and minimum rotations are equal to each other *. 



6. Description of the Apparatus. — The mirrors were ground 

 on iron rings which were encircled by seven layers of wind- 

 ings of copper wire 1*5 to 2 millim. thick. Fig. 2 gives a 



* For complete proofs of these statements the original memoir must be 

 consulted. 



